Last visit was: 17 Jul 2024, 19:44 It is currently 17 Jul 2024, 19:44
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Kudos
Tags:
Show Tags
Hide Tags
User avatar
Senior Manager
Senior Manager
Joined: 09 Jul 2013
Status:1,750 Q's attempted and counting
Affiliations: University of Florida
Posts: 421
Own Kudos [?]: 3007 [18]
Given Kudos: 630
Location: United States (FL)
GMAT 1: 570 Q42 V28
GMAT 2: 610 Q44 V30
GMAT 3: 600 Q45 V29
GMAT 4: 590 Q35 V35
GPA: 3.45
WE:Accounting (Accounting)
Send PM
User avatar
Intern
Intern
Joined: 14 Aug 2013
Posts: 23
Own Kudos [?]: 155 [3]
Given Kudos: 4
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE:Consulting (Consumer Electronics)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30830 [3]
Given Kudos: 799
Location: Canada
Send PM
Intern
Intern
Joined: 02 Aug 2019
Posts: 4
Own Kudos [?]: 3 [1]
Given Kudos: 22
Send PM
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
1
Kudos
GMATPrepNow wrote:
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3
(2) x - y = 3



Target question: What is the value of (x+y)²?

Given: x² - y² = 27

Statement 1: y = 3
Take x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 18
So, EITHER x = √18 OR x = -√18
Let's test each case:
Case a: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case, the answer to the target question is (√18 + 3)²
Case b: x = -√18 and y = 3. So, (x + y)² = (-√18 + 3)². So, in this case, the answer to the target question is (-√18 + 3)²
NOTE: We need not actually calculate the values of (√18 + 3)² and (-√18 + 3)². We need only see that the two values are DIFFERENT
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 3
Take x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So, the answer to the target question is 81
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent


Posted from my mobile device
Intern
Intern
Joined: 21 May 2016
Posts: 6
Own Kudos [?]: 4 [1]
Given Kudos: 46
GMAT 1: 710 Q50 V36
Send PM
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
1
Kudos
the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.

Posted from my mobile device
User avatar
Senior Manager
Senior Manager
Joined: 09 Jul 2013
Status:1,750 Q's attempted and counting
Affiliations: University of Florida
Posts: 421
Own Kudos [?]: 3007 [1]
Given Kudos: 630
Location: United States (FL)
GMAT 1: 570 Q42 V28
GMAT 2: 610 Q44 V30
GMAT 3: 600 Q45 V29
GMAT 4: 590 Q35 V35
GPA: 3.45
WE:Accounting (Accounting)
Send PM
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
1
Bookmarks
Official Explanation

Answer: B
- First, recognize that x^2 - y^2 = (x + y)(x - y). That makes the expression a little more similar to what we're looking for -- both this and (x + y)^2 contain a (x + y) term.

Statement (1) is insufficient. If y = 3, then x^2 - 9 = 27, so x^2 = 36. x must be either 6 or -6. If x = 6, the answer is (6 + 3)^2 = 81, but if x = -6, the answer is (-6 + 3)^2 = 9.

Statement (2) is sufficient. Since (x + y)(x - y) = 27, if (x - y) = 3, then (x + y) = 9. We're looking for (x + y)^2, which is 9^2 = 81. Choice (B) is correct.
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2551 [0]
Given Kudos: 459
Location: India
Send PM
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3



GH-06.05.13 | OE to follow


x^2 - y^2 = 27 OR (x+y)(x-y) = 27
We need to find (x+y)^2, for which we need (x+y). Here various cases are possible for (x+y) and (x-y).. Eg, former could be 9 and latter 3 or former could be 3 and latter 9 or former could be -3 and latter -9.

(1) y=3. Substituting this we get
x^2 - 3^2 = 27 OR x^2 = 27+9=36. Two values are possible for x here: 6 and -6, this will give two different answers for x+y. So Insufficient

(2) x-y=3. Substituting this we get
(x+y)*3 = 27 or x+y =9. So we can get (x+y)^2. Sufficient.

Hence B answer
Tutor
Joined: 17 Sep 2014
Posts: 1245
Own Kudos [?]: 967 [0]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Send PM
If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
Expert Reply
Analyzing the question:
To figure out \((x + y)^2\) we only need \(x + y.\) Since we are given \(x^2 - y^2 = (x - y)(x + y) = 27\), knowing \(x - y\) would also give \(x + y\) from that equation. Therefore we are trying to find \(x - y\), \(x + y\), or both values of x and y.

Statement 1:
(1) This gives us \(x^2 = 36\) but we don’t know if x is positive or negative. The two solutions give different values of \((x + y)^2\) so this is insufficient.

Statement 2:
(2) As stated above this is sufficient.

Answer: B
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30830 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
Expert Reply
Top Contributor
ankitiofs wrote:
the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.

Posted from my mobile device


Thanks for the heads up!
I have edited my response accordingly.

Cheers,
Brent
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34005
Own Kudos [?]: 852 [0]
Given Kudos: 0
Send PM
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ? [#permalink]
Moderator:
Math Expert
94384 posts